Suppose we have white gaussian noise $N(t)$ which is band-limited to B Hz and flat PSD with amplitude $\frac{\mathscr N}{2}$ in the freq. range [-B, B]. we do sampling from N(t) at Nyquist rate, $f_s=2B$, samples are independent, we know that differential entropy of N(t) is:
$ \frac{1}{2}log_2 (2\pi e \mathscr N B) $ (bits)
given this information, one claims that entropy of each sample is also $ \frac{1}{2}log_2 (2\pi e \mathscr N B) $ (same as entropy of N(t)) and so the entropy of the whole 2B samples is $ 2B \times \frac{1}{2}log_2 (2\pi e \mathscr N B) $ bits/sec. I don't know how to obtain entropy of each sample but intuitively I expect that each sample entropy must be $\frac{1}{2B} $ times the entropy of N(t). I appreciate if anyone can proof how we can obtain entropy of each sample given above scenario. thanks